No-flux boundary conditions are used on both sides of the domain.
The domain is resolved using 32 elements with polynomial order 4.
Time integration is performed using the fourth-order five-stage low storage
Runge–Kutta (LSRK54) method from [1]} with CFL = 0.2.
To assess the impact of quadrature rule accuracy,
simulations using two sets of quadrature points are considered: \(N+1\) 
Legendre–Gauss–Lobatto (LGL) points and a more accurate \(N+2\)  point Gauss quadrature.
<FIGURE><FIGURE>